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1.
The relation in which the vertical and horizontal gradients of potential field data measured along a profile across a two‐dimensional source are a Hilbert transform pair is re‐established using complex domain mathematics. In addition, a relation between the measured field and its vertical gradient in terms of a closed‐form formula is also established. The formula is based on hypersingular or Hadamard's finite‐part integral. To estimate the vertical gradient directly from the field data, Linz's algorithm of computing Hadamard's finite‐part integral is implemented. Numerical experiments are conducted on synthetically generated total magnetic intensity data with a mild level of noise contamination. A model of a magnetically polarised vertical thin sheet buried at a finite depth within a non‐magnetic half‐space was considered in generating the synthetic response. The results from numerical experiments on the mildly noise‐contaminated synthetic response are compared with those from using classical Fourier and robust regularised Hilbert transform‐based techniques.  相似文献   

2.
We have developed a least‐squares minimization approach to depth determination using numerical second horizontal derivative anomalies obtained from magnetic data with filters of successive window lengths (graticule spacings). The problem of depth determination from second‐derivative magnetic anomalies has been transformed into finding a solution to a non‐linear equation of the form, f(z) = 0. Formulae have been derived for a sphere, a horizontal cylinder, a dike and a geological contact. Procedures are also formulated to estimate the magnetic angle and the amplitude coefficient. We have also developed a simple method to define simultaneously the shape (shape factor) and the depth of a buried structure from magnetic data. The method is based on computing the variance of depths determined from all second‐derivative anomaly profiles using the above method. The variance is considered a criterion for determining the correct shape and depth of the buried structure. When the correct shape factor is used, the variance of depths is less than the variances computed using incorrect shape factors. The method is applied to synthetic data with and without random errors, complicated regionals, and interference from neighbouring magnetic rocks. Finally, the method is tested on a field example from India. In all the cases examined, the depth and the shape parameters are found to be in good agreement with the actual parameters.  相似文献   

3.
Recent improvements in the local wavenumber approach have made it possible to estimate both the depth and model type of buried bodies from magnetic data. However, these improvements require calculation of third‐order derivatives of the magnetic field, which greatly enhances noise. As a result, the improvements are restricted to data of high quality. We present an alternative method to estimate both the depth and model type using the first‐order local wavenumber approach without the need for third‐order derivatives of the field. Our method is based on normalization of the first‐order local wavenumber anomalies and provides a generalized equation to estimate the depth of some 2D magnetic sources regardless of the source structure. Information about the nature of the sources is obtained after the source location has been estimated. The method was tested using synthetic magnetic anomaly data with random noise and using three field examples.  相似文献   

4.
Nonparametric inverse methods provide a general framework for solving potential‐field problems. The use of weighted norms leads to a general regularization problem of Tikhonov form. We present an alternative procedure to estimate the source susceptibility distribution from potential field measurements exploiting inversion methods by means of a flexible depth‐weighting function in the Tikhonov formulation. Our approach improves the formulation proposed by Li and Oldenburg (1996, 1998) , differing significantly in the definition of the depth‐weighting function. In our formalism the depth weighting function is associated not to the field decay of a single block (which can be representative of just a part of the source) but to the field decay of the whole source, thus implying that the data inversion is independent on the cell shape. So, in our procedure, the depth‐weighting function is not given with a fixed exponent but with the structural index N of the source as the exponent. Differently than previous methods, our choice gives a substantial objectivity to the form of the depth‐weighting function and to the consequent solutions. The allowed values for the exponent of the depth‐weighting function depend on the range of N for sources: 0 ≤N≤ 3 (magnetic case). The analysis regarding the cases of simple sources such as dipoles, dipole lines, dykes or contacts, validate our hypothesis. The study of a complex synthetic case also proves that the depth‐weighting decay cannot be necessarily assumed as equal to 3. Moreover it should not be kept constant for multi‐source models but should instead depend on the structural indices of the different sources. In this way we are able to successfully invert the magnetic data of the Vulture area, Southern Italy. An original aspect of the proposed inversion scheme is that it brings an explicit link between two widely used types of interpretation methods, namely those assuming homogeneous fields, such as Euler deconvolution or depth from extreme points transformation and the inversion under the Tikhonov‐form including a depth‐weighting function. The availability of further constraints, from drillings or known geology, will definitely improve the quality of the solution.  相似文献   

5.
Magnetic data analysis at low latitudes using magnitude transforms   总被引：2，自引：0，他引：2  
Magnitude transforms include magnitude magnetic anomalies (MMA), their gradients and Laplacians. They can be calculated from the total magnetic anomalies or other component anomalies. Magnitude magnetic anomalies have a space distribution different from that of the component anomalies. Their values are non‐negative and their respective patterns are similar to the positive gravity anomalies. Magnitude transforms are an effective tool for magnetic data analysis due to their simplified pattern and direct correlation with the space location of the source. They have advantages over the traditionally used reduction‐to‐the‐pole (RTP) transform, especially at low magnetic latitudes. The calculation of magnitudes of the anomalous field requires the total field data to be transformed into the component anomalies, while the reduction‐to‐the‐pole transform also includes a rotation of the magnetization vector, the orientation of which is usually assumed. For equal latitudes, the transfer functions of component‐component transforms in the frequency domain show better stability than the component‐component‐rotation transfer function. This is illustrated by a comparison of analytical expressions, and synthetic models of magnetic fields. The Dixon seamount case shows the possibilities for an improved data analysis and more confident source recognition at low latitudes using magnetic transforms.  相似文献   

6.
In this paper, we describe a non‐linear constrained inversion technique for 2D interpretation of high resolution magnetic field data along flight lines using a simple dike model. We first estimate the strike direction of a quasi 2D structure based on the eigenvector corresponding to the minimum eigenvalue of the pseudogravity gradient tensor derived from gridded, low‐pass filtered magnetic field anomalies, assuming that the magnetization direction is known. Then the measured magnetic field can be transformed into the strike coordinate system and all magnetic dike parameters – horizontal position, depth to the top, dip angle, width and susceptibility contrast – can be estimated by non‐linear least squares inversion of the high resolution magnetic field data along the flight lines. We use the Levenberg‐Marquardt algorithm together with the trust‐region‐reflective method enabling users to define inequality constraints on model parameters such that the estimated parameters are always in a trust region. Assuming that the maximum of the calculated gzz (vertical gradient of the pseudogravity field) is approximately located above the causative body, data points enclosed by a window, along the profile, centred at the maximum of gzz are used in the inversion scheme for estimating the dike parameters. The size of the window is increased until it exceeds a predefined limit. Then the solution corresponding to the minimum data fit error is chosen as the most reliable one. Using synthetic data we study the effect of random noise and interfering sources on the estimated models and we apply our method to a new aeromagnetic data set from the Särna area, west central Sweden including constraints from laboratory measurements on rock samples from the area.  相似文献   

7.
The voluminous gravity and magnetic data sets demand automatic interpretation techniques like Naudy, Euler and Werner deconvolution. Of these techniques, the Euler deconvolution has become a popular choice because the method assumes no particular geological model. However, the conventional approach to solving Euler equation requires tentative values of the structural index preventing it from being fully automatic and assumes a constant background that can be easily violated if the singular points are close to each other. We propose a possible solution to these problems by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization technique like conjugate gradient. This technique is applied to a published synthetic data set where the magnetic anomalies were modeled for a complex assemblage of simple magnetic bodies. The results for close by singular points are superior to those obtained by assuming linear background. We also applied the technique to a magnetic data set collected along the western continental margin of India. The results are in agreement with the regional magnetic interpretation and the bathymetric expressions.  相似文献   

8.
The calculable magnitudes of the anomalous magnetic field from simple 2D sources and their gradients and Laplacians appear as ratios that can be synthesized in functional forms, corresponding to the different source shapes. Field components and first‐order derivatives are involved in the inversion procedures presented. The structural index and source depth are estimated independently of each other. The applied functions allow magnetic profiles and magnetic maps to be shape‐ and depth‐converted with immediate imaging of the inversion results. The contours of these functions outline elongated loops around the 2.5D anomaly axis on magnetic maps. The width of the loops reflects the depth and structural index N of the source in the scale units of the inverted map. Model and field tests illustrate the effectiveness of this approach for fast automatic inversion of large sets of magnetic data for depth, shape, length and location of simple sources.  相似文献   

9.
The depth‐integrated momentum and kinetic energy equations contain velocity correlation terms that involve products of local deviations in velocity components about depth‐averaged values. Based on velocity data obtained from North Boulder Creek, Colorado, a simple scaling analysis suggests that certain of these terms, which normally can be neglected in the case of smooth channels, can be significant parts of the momentum and energy balances in steep, rough channels owing to the occurrence of non‐logarithmic velocity profiles. A linearized version of the kinetic energy equation suggests that, for flow accelerations over small‐amplitude bed forms, the energy of the mean motion is spatially partitioned between a form involving the depth‐averaged velocity and a form involving the deviatoric part of the velocity profile; this partitioning is associated with spatial variations in the uniformity of the vertical profile of the streamwise velocity. These points are consistent with published flume measurements involving flow over sand‐roughened dunes, and with published field measurements of flow over a gravel bar. Copyright © 2000 John Wiley & Sons, Ltd.  相似文献   

10.
The total mean‐square error (MSE) of the estimated model, defined as the sum of the standard model variance and the bias variance, is used to define the truncation level of the singular‐value decomposition to give a reasonable balance between model resolution and model variance. This balance is determined largely by the data and no further assumptions are necessary except that the bias terms are estimated sufficiently well. This principle has been tested on the 1D magnetotelluric inverse problem with special emphasis on high‐frequency radio magnetotelluric (RMT) data. Simulations clearly demonstrate that the method provides a good balance between resolution and variance. Starting from a homogeneous half‐space, the best solution is sought for a fixed set of singular values. The model variance is estimated from the sum of the inverse eigenvalues squared, up to a certain threshold, and the bias variance is estimated from the model projections on the remaining eigenvectors. By varying the threshold, the minimum of the MSE is found for an increasing number of fixed singular values until the number of active singular values becomes greater than or equal to the estimated number. As a side‐effect, the depth of penetration of a given set of measurements can be estimated very efficiently by simply noting at which depth the final model deviates little from the starting homogeneous half‐space model. A suite of synthetic data is inverted and an example of inversion of one site is shown to illustrate how the truncation is carried out as the non‐linear inversion process proceeds. A field example with a profile across a plume of contaminated groundwater in the Netherlands shows good agreement with the electrical resistivity obtained in a nearby borehole.  相似文献   

11.
We have developed three different least-squares approaches to determine successively: the depth, magnetic angle, and amplitude coefficient of a buried sphere from a total magnetic anomaly. By defining the anomaly value at the origin and the nearest zero-anomaly distance from the origin on the profile, the problem of depth determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(z)=0. Knowing the depth and applying the least-squares method, the magnetic angle and amplitude coefficient are determined using two simple linear equations. In this way, the depth, magnetic angle, and amplitude coefficient are determined individually from all observed total magnetic data. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal, West Africa. In all cases, the depth solutions are in good agreement with the actual ones.  相似文献   

12.
Potential field data such as geoid and gravity anomalies are globally available and offer valuable information about the Earth's lithosphere especially in areas where seismic data coverage is sparse. For instance, non‐linear inversion of Bouguer anomalies could be used to estimate the crustal structures including variations of the crustal density and of the depth of the crust–mantle boundary, that is, Moho. However, due to non‐linearity of this inverse problem, classical inversion methods would fail whenever there is no reliable initial model. Swarm intelligence algorithms, such as particle swarm optimisation, are a promising alternative to classical inversion methods because the quality of their solutions does not depend on the initial model; they do not use the derivatives of the objective function, hence allowing the use of L1 norm; and finally, they are global search methods, meaning, the problem could be non‐convex. In this paper, quantum‐behaved particle swarm, a probabilistic swarm intelligence‐like algorithm, is used to solve the non‐linear gravity inverse problem. The method is first successfully tested on a realistic synthetic crustal model with a linear vertical density gradient and lateral density and depth variations at the base of crust in the presence of white Gaussian noise. Then, it is applied to the EIGEN 6c4, a combined global gravity model, to estimate the depth to the base of the crust and the mean density contrast between the crust and the upper‐mantle lithosphere in the Eurasia–Arabia continental collision zone along a 400 km profile crossing the Zagros Mountains (Iran). The results agree well with previously published works including both seismic and potential field studies.  相似文献   

13.
We have developed an automatic method to determine the depth of a buried sphere from numerical second horizontal derivative anomalies obtained from total field magnetic data. The method is based on using a relationship between the depth and a combination of observations at symmetric points with respect to the coordinate of the projection of the center of the source in the plane of the measurement points with a free parameter (graticule spacing). The problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of f(z) = 0. Procedures are also formulated to determine the magnetic moment and the effective angle of magnetization. The method is applied to synthetic examples with and without random errors and tested on a field example from Senegal. In all cases, the depth solutions are in good agreement with the actual ones.  相似文献   

14.
The application of semi‐automatic interpretation techniques to potential field data can be of significant assistance to a geophysicist. This paper generalizes the magnetic vertical contact model tilt‐depth method to gravity data using a vertical cylinder and buried sphere models. The method computes the ratio of the vertical to the total horizontal derivative of data and then identifies circular contours within it. Given the radius of the contour and the contour value itself, the depth to the source can be determined. The method is applied both to synthetic and gravity data from South Africa. The Matlab source code can be obtained from the author upon request.  相似文献   

15.
-- A technique to estimate the depth to anomalous sources from the scaling power spectra of long nonstationary gravity profiles is presented. The nonstationary profile is divided into piecewise stationary segments based on the criterion of optimum gate length in which the time-varying and time-invariant autocorrelation functions are similar. The division of a nonstationary into piecewise stationary allows identification of the portion of the crust with different geological histories, and using the stationary portion of the gravity profiles, more consistent depths to the anomalous sources have been obtained. The technique is tested with the synthetic gravity profile and applied along the Jaipur-Raipur geotransect in western and central India. The geotransect has been divided into four stationary parts: Vindhyan low, Bundelkhand low, Narmada rift and Chhattisgarh basin; each section corresponding to a different geological formation. Forward modeling of gravity data using results of each stationary section is carried out to propose the subsurface structure along the Jaipur-Raipur transect.  相似文献   

16.
To better understand (and correct for) the factors affecting the estimation of attenuation (Q), we simulate subsurface wave propagation with the Weyl/Sommerfeld integral. The complete spherical wavefield emanating from a P‐wave point source surrounded by a homogeneous, isotropic and attenuative medium is thus computed. In a resulting synthetic vertical seismic profile, we observe near‐field and far‐field responses and a 90° phase rotation between them. Depth dependence of the magnitude spectra in these two depth regions is distinctly different. The logarithm of the magnitude spectra shows a linear dependence on frequency in the far‐field but not in those depth regions where the near‐field becomes significant. Near‐field effects are one possible explanation for large positive and even negative Q‐factors in the shallow section that may be estimated from real vertical seismic profile data when applying the spectral ratio method. We outline a near‐field compensation technique that can reduce errors in the resultant Q estimates.  相似文献   

17.
This paper presents a simple method for shape and depth determination of a buried structure from residual gravity anomalies along profile. The method utilizes the anomaly values of the origin and characteristic points of the profile to construct a relationship between the shape factor and depth of the causative source. For fixed points, the depth is determined for each shape factor. The computed depths are then plotted against the shape factor representing a continuous monotonically increasing curve. The solution for the shape and depth of the buried structure is then read at the common intersection point of the depth curves. This method is applied to synthetic data with and without random errors. Finally, the validity of the method is tested on two field examples from the USA.  相似文献   

18.
A geophysical interpretative method is proposed to depth, amplitude coefficient (effective magnetization intensity), and index parameter (effective magnetization inclination) determination of a buried structure from magnetic field data anomaly due to a fault, a thin dike or a sphere-like structure. The method is based on the nonlinearly constrained mathematical modelling and also on the stochastic optimization approaches. The proposed interpretative method was first tested on a theoretical synthetic model with different random errors, where a very close agreement was obtained between the assumed and the evaluated parameters. The validity of this method was also tested on practical field data taken from United States, Australia, India and Brazil, where available magnetic data existed and were previously analyzed by different interpretative methods. The agreement between the results obtained by our developed method and those obtained by the other geophysical methods is good.  相似文献   

19.
The recent use of marine electromagnetic technology for exploration geophysics has primarily focused on applying the controlled source electromagnetic method for hydrocarbon mapping. However, this technology also has potential for structural mapping applications, particularly when the relative higher frequency controlled source electromagnetic data are combined with the lower frequencies of naturally occurring magnetotelluric data. This paper reports on an extensive test using data from 84 marine controlled source electromagnetic and magnetotelluric stations for imaging volcanic sections and underlying sediments on a 128‐km‐long profile. The profile extends across the trough between the Faroe and Shetland Islands in the North Sea. Here, we focus on how 2.5D inversion can best recover the volcanic and sedimentary sections. A synthetic test carried out with 3D anisotropic model responses shows that vertically transverse isotropy 2.5D inversion using controlled source electromagnetic and magnetotelluric data provides the most accurate prediction of the resistivity in both volcanic and sedimentary sections. We find the 2.5D inversion works well despite moderate 3D structure in the synthetic model. Triaxial inversion using the combination of controlled source electromagnetic and magnetotelluric data provided a constant resistivity contour that most closely matched the true base of the volcanic flows. For the field survey data, triaxial inversion of controlled source electromagnetic and magnetotelluric data provides the best overall tie to well logs with vertically transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data a close second. Vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data provided the best interpreted base of the volcanic horizon when compared with our best seismic interpretation. The structural boundaries estimated by the 20‐Ω·m contour of the vertical resistivity obtained by vertical transverse isotropy inversion of controlled source electromagnetic and magnetotelluric data gives a maximum geometric location error of 11% with a mean error of 1.2% compared with the interpreted base of the volcanic horizon. Both the model study and field data interpretation indicate that marine electromagnetic technology has the potential to discriminate between low‐resistivity prospective siliciclastic sediments and higher resistivity non‐prospective volcaniclastic sediments beneath the volcanic section.  相似文献   

20.
This paper presents a new inversion method for the interpretation of 2D magnetic anomaly data, which uses the combination of the analytic signal and its total gradient to estimate the depth and the nature (structural index) of an isolated magnetic source. However, our proposed method is sensitive to noise. In order to lower the effect of noise, we apply upward continuation technique to smooth the anomaly. Tests on synthetic noise-free and noise corrupted magnetic data show that the new method can successfully estimate the depth and the nature of the causative source. The practical application of the technique is applied to measured magnetic anomaly data from Jurh area, northeast China, and the inversion results are in agreement with the inversion results from Euler deconvolution of the analytic signal.  相似文献   

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